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ExtremeBDS [4]
3 years ago
5

A circle is centered on point B. Points A, C and D lie on its circumference.

Mathematics
1 answer:
IRISSAK [1]3 years ago
3 0

Given:

A circle is centered on point B.

Points A, C and D lie on its circumference.

If m\angle ABC measures 40°.

To find:

The m\angle ADC.

Solution:

Central angle theorem: According to this theorem, the central angle is equal to the twice of inscribed angle on the same intercepted arc.

In the given figure \angle ABC is the central angle and m\angle ADC is the inscribed angle on the same arc AC.

Using central angle theorem, we get

m\angle ABC=2m\angle ADC

40^\circ=2m\angle ADC

\dfrac{40^\circ}{2}=m\angle ADC

20^\circ=m\angle ADC

Therefore, the measure of angle ADC is 20°.

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